Cyber Synchronous Machine (Cybersync Machine)

ABSTRACT

This invention discloses a controller and method for a cyber synchronous machine (CSM, in short, cybersync machine), namely, a power electronic converter that is seamlessly equipped with computational algorithms (i.e., the controller) to represent the intrinsic and fundamental principles of physical synchronous machines. The CSM can be operated in the grid-connected mode or the islanded mode to take part in the regulation of the frequency and the voltage. The controller also includes auxiliary blocks to achieve self-synchronization without measuring or estimating the grid frequency and the regulation of real power and reactive power to the given reference values without static errors. The control signal for the power electronic converter can be the output voltage generated by the engendering block or the sum of the output voltage and the virtual current. A unique feature of the disclosed CSM is that, if the system it is connected to is passive, then the whole system is passive and, hence, is guaranteed to be stable.

CROSS-REFERENCE TO RELATED APPLICATIONS

This nonprovisional patent application claims the benefit of andpriority under 35 U.S. Code 119 (b) to U.K. Patent Application No.GB1708886.5 filed on Jun. 4, 2017, entitled “Cyber Synchronous Machine(Cybersync Machine)”, the contents of which are all hereby incorporatedby reference herein in its entirety.

TECHNICAL FIELD

This invention is concerned with the control and operation of powerelectronic converters. Possible application fields include renewableenergy, such as wind, solar and wave energy, electrical vehicles, energystorage systems, aircraft power systems, different types of loads thatrequire power electronic converters, data centers and so on.

BACKGROUND

Power systems are going through a paradigm change. At the moment, thefrequency of a power system is controlled by regulating a small numberof large synchronous generators and most loads do not take part in thefrequency control of the system. But now, the landscape of power systemsis rapidly changing. Various non-synchronous distributed energyresources (DER), including renewables, electric vehicles and energystorage systems, are being connected to power systems. Moreover, mostloads that do not take part in frequency control now are expected totake part in frequency control in the future. Hence, the number ofactive players to take part in frequency control in the future couldeasily reach millions, which imposes unprecedented challenges to thefrequency stability of future power systems. The fundamental challengebehind this paradigm change is that future power systems will be powerelectronics-based, instead of electric machines-based, with millions ofrelatively small, non-synchronous and incompatible players. For example,on the supply side, most DERs are connected to power systems throughpower electronic converters. In transmission and distribution networks,many power electronic converters, such as HVDC links and FACTS devices,are being introduced to electronically control power systems in order toimprove efficiency and controllability. On the load side, most loadswill be connected to the grid through power electronic converters aswell. For example, motors, which consume over 50% of electricity, aremuch more efficient when equipped with motor drives; Internet devices,which consume over 10% of electricity, have front-end power electronicconverters; lighting devices, which consume about 20% of electricity,are being replaced with LED lights, which have front-end powerelectronic converters as well. The integration of power electronicconverters into the electrical grid for distributed generation (DG),often by means of microgrids, has been a topic of intensive research anddevelopment.

Most of the converters nowadays are controlled to behave as currentsources, through controlling the current exchanged with the grid.However, this makes them incompatible with the power systems, which aredominated by voltage sources.

Power electronic converters could play a similar role as synchronousgenerators in conventional power systems. Hence, it is reasonable toadopt some of the well established concepts and principles in powersystems to control power electronic converters. Recently, it has beenshown by the inventor of this disclosure that the well-known droopcontrol strategy structurally resembles the widely-used phase-lockedloop and that the conventional synchronous machines resemble thephase-locked loop as well. What is common among these different conceptsis their intrinsic synchronization mechanism. The inventor of thisdisclosure has also shown that this synchronization mechanism should andcould be adopted to build future power systems that are dominated bypower electronic converters.

BRIEF SUMMARY

The following summary is provided to facilitate an understanding of someof the innovative features unique to the disclosed embodiments and isnot intended to be a full description. A full appreciation of thevarious aspects of the embodiments disclosed herein can be gained bytaking the entire specification, claims, drawings, and abstract as awhole.

This invention discloses a controller and method for a cyber synchronousmachine (CSM, in short, cybersync machine), namely, a power electronicconverter that is seamlessly integrated with computational algorithms(i.e. the controller) to represent the intrinsic and fundamentalprinciples of physical synchronous machines, in particular, thesynchronization mechanism. The controller consists of (1) atorque-frequency channel to regulate the frequency according to thetorque (equivalently, the real power) set-point, (2) a quorte-fluxchannel to regulate the flux (equivalently, the voltage amplitude)according to the quorte (equivalently, the reactive power) set-point,(3) an engendering block that generates an output voltage according tothe frequency generated in the torque-frequency channel and the fluxgenerated in the quorte-flux channel, and also the torque and quortefeedback signals with the additional input of current, and (4) a virtualimpedance to generate a virtual current according to the difference oftwo voltages. The CSM can be operated to regulate the real power andreactive power according to the given real power and reactive powerreferences (called in the set mode), to take part in the regulation ofthe frequency and the voltage (called in the droop mode), and tosynchronize with the grid without estimating or measuring the gridfrequency (called in the self-synchronization mode). What is crucial forthe disclosed invention is that if the system to which the disclosed CSMis connected is passive, then the whole system is passive and, hence, isguaranteed to be stable.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures further illustrate the disclosed embodimentsand, together with the detailed description of the disclosedembodiments, serve to explain the principles of the present invention.

FIG. 1 shows the typical system connected to the grid with the voltage egenerated by a power electronic converter.

FIG. 2 shows the disclosed controller of a cyber synchronous machine.

FIG. 3 illustrates a possible implementation of the passive blocks Σ_(ω)and Σ_(φ) in the controller.

FIG. 4 illustrates the simulation results: (a) Active power P; (b)Reactive power Q; (c) Frequency f; (d) Flux φ; (e) Phase-A voltage e_(a)(rms); and (f) Phase-A voltage v_(a) (rms).

DETAILED DESCRIPTION

The particular values and configurations discussed in these non-limitingexamples can be varied and are cited merely to illustrate at least oneembodiment and are not intended to limit the scope thereof.

The embodiments will now be described more fully hereinafter withreference to the accompanying drawings, in which illustrativeembodiments of the invention are shown. The embodiments disclosed hereincan be embodied in many different forms and should not be construed aslimited to the embodiments set forth herein; rather, these embodimentsare provided so that this disclosure will be thorough and complete, andwill fully convey the scope of the invention to those skilled in theart.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a,” “an,” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this invention belongs. It will befurther understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

Subject matter will now be described more fully hereinafter withreference to the accompanying drawings, which form a part hereof, andwhich show, by way of illustration, specific example embodiments.Subject matter may, however, be embodied in a variety of different formsand, therefore, covered or claimed subject matter is intended to beconstrued as not being limited to any example embodiments set forthherein; example embodiments are provided merely to be illustrative.Likewise, a reasonably broad scope for claimed or covered subject matteris intended. Among other things, for example, subject matter may beembodied as methods, devices, components, or systems. Accordingly,embodiments may, for example, take the form of hardware, software,firmware or any combination thereof (other than software per se). Thefollowing detailed description is, therefore, not intended to be takenin a limiting sense.

Throughout the specification and claims, terms may have nuanced meaningssuggested or implied in context beyond an explicitly stated meaning.Likewise, the phrase “in one embodiment” as used herein does notnecessarily refer to the same embodiment and the phrase “in anotherembodiment” as used herein does not necessarily refer to a differentembodiment. It is intended, for example, that claimed subject matterinclude combinations of example embodiments in whole or in part.

In general, terminology may be understood at least in part from usage incontext. For example, terms such as “and,” “or,” or “and/or” as usedherein may include a variety of meanings that may depend at least inpart upon the context in which such terms are used. Typically, “or” ifused to associate a list, such as A, B, or C, is intended to mean A, B,and C, here used in the inclusive sense, as well as A, B, or C, hereused in the exclusive sense. In addition, the term “one or more” as usedherein, depending at least in part upon context, may be used to describeany feature, structure, or characteristic in a singular sense or may beused to describe combinations of features, structures or characteristicsin a plural sense. Similarly, terms, such as “a,” “an,” or “the,” again,may be understood to convey a singular usage or to convey a pluralusage, depending at least in part upon context. In addition, the term“based on” may be understood as not necessarily intended to convey anexclusive set of factors and may, instead, allow for existence ofadditional factors not necessarily expressly described, again, dependingat least in part on context.

The system under consideration is shown in FIG. 1. A three-phase powerelectronic converter is represented by ideal voltage sources e=[e_(a)e_(b) e_(c)]^(T), without showing the details of the converter bridges,because the switching effect of the power semiconductor devices can beneglected for the purpose of control design as long as the controllercan generate the right voltage e and the switching frequency is highenough. The converter may be operated in the grid-connected mode or inthe islanded mode. i.e., with the main breaker ON or OFF. The case witha single phase or multiple phases can be treated in a similar way andthis disclosure takes three-phase systems as an example.

The converter-side elements L₁ and R₁ and the capacitor C_(f) form a LCfilter to filter out the switching ripples. The supply-side elements L₂and R₂ can be regarded as an additional inductor that is part of an LCLfilter and/or a coupling transformer.

The objective of this invention is to disclose a controller and methodthat generates an output voltage e to render the system shown in FIG. 1passive and hence stable.

The Disclosed Controller

The disclosed controller is shown in FIG. 2. The controller consists ofthe control block Σ_(C), the engendering block Σ_(e) and auxiliaryblocks including I_(ω), I_(φ) and Z(s) to achieve self-synchronizationwithout measuring or estimating the grid frequency and regulation ofreal power and reactive power. The block Σ_(C) has two channels, namelythe torque-frequency channel and the quorte-flux channel, which includessubsystems Σ_(ω) and Σ_(φ), respectively. The subsystem E_(ω) is used tosynthesize the frequency ω and the subsystem E_(φ) is used to synthesizethe flux φ. The engendering block Σ_(e) synthesizes an output voltage eaccording to the frequency ω and the flux φ, with the phase angle θ ofthe generated voltage e satisfying {dot over (θ)}=ω, and also providesthe feedback for the two control channels. The auxiliary block Z(s) is avirtual impedance introduced to generate a virtual current i_(v) toreplace the grid current i during the self-synchronization process. Theauxiliary blocks I_(ω) and I_(φ) include a resettable integrator toregulate T and Γ according to the given set-points T_(set) and Γ_(set),which correspond to the desired real power and reactive power.

The Engendering Block Σ_(e):

The ghost operator g is an operator that shifts the phase of a sine orcosine function by

$\frac{\pi}{2}$

rad leading. Define the sinusoidal and cosinusoidal signals

-   -   {tilde over (z)}=sin θ and {tilde over (z)}_(g)=g{tilde over        (z)}=cos θ.        In other words, {tilde over (z)}_(g) is obtained via applying        the ghost operator g to {tilde over (z)}. Note that {tilde over        (z)} and {tilde over (z)}_(g) are actually the states of the        oscillator

$\begin{matrix}{\overset{.}{\begin{bmatrix}\overset{\sim}{z} \\{\overset{\sim}{z}}_{g}\end{bmatrix}} = {\begin{bmatrix}0 & \omega \\{- \omega} & 0\end{bmatrix}\begin{bmatrix}\overset{\sim}{z} \\{\overset{\sim}{z}}_{g}\end{bmatrix}}} & (1)\end{matrix}$

with the oscillating frequency ω={dot over (θ)} being the input.Moreover, define the following sinusoidal vector

$\begin{matrix}{z = {\left\lbrack {\sin \mspace{14mu} \theta \mspace{14mu} \sin \mspace{14mu} \left( {\theta - \frac{2\pi}{3}} \right)\mspace{14mu} \sin \mspace{14mu} \left( {\theta + \frac{2\pi}{3}} \right)} \right\rbrack^{T}.}} & (2)\end{matrix}$

to represent normalized three-phase voltages. Furthermore, denotez_(g)=gz. Then

$z_{g} = {{gz} = \left\lbrack {\cos \mspace{14mu} \theta \mspace{14mu} \cos \mspace{14mu} \left( {\theta - \frac{2\pi}{3}} \right)\mspace{14mu} \cos \mspace{14mu} \left( {\theta + \frac{2\pi}{3}} \right)} \right\rbrack^{T}}$

is a cosinusoidal vector corresponding to a three-phase system. It iseasy to see that the sinusoidal and cosinusoidal vectors z and z_(g) canbe described by the linear combination of the oscillator states as

$\begin{matrix}{\begin{bmatrix}z \\z_{g}\end{bmatrix} = {{\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} & 0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}} \\0 & {- \frac{\sqrt{3}}{2}} & \frac{\sqrt{3}}{2} & 1 & {- \frac{1}{2}} & {- \frac{1}{2}}\end{bmatrix}^{T}\begin{bmatrix}\overset{\sim}{z} \\{\overset{\sim}{z}}_{g}\end{bmatrix}}.}} & (3)\end{matrix}$

The output voltage e is designed as

e=Ez,  (4)

with

E=ωφ

being the amplitude of the output voltage, which is the product of thefrequency ω and the flux φ. Because the frequency ω only varies in avery small range during normal operation, the voltage E is mainlydetermined by the flux φ. Denote e_(g)=ge to represent the “ghost”three-phase voltages, which are 90° leading e. Then,

e _(g) =ge=Ez _(g).  (5)

For the three-phase converter shown in FIG. 1, the real power and thereactive power at the mid-point of the conversion legs can be obtained,respectively, as

P=

i,e

, Q=−

i,e _(g)

.

Hence, the real power and the reactive power are

P=ωφ

i,z

Tω, Q=−ωφ

i,z _(g)

Γφ,  (6)

where

T=φ(i,z)=φz ^(T) i  (7)

resembles the electromagnetic torque of a synchronous machine and

Γ=−ω

i,z _(g)

−ωz _(g) ^(T) i  (8)

is a quantity dual to the torque T, for which the word quorte is coinedto represent its duality to the torque. Since the frequency ω and theflux φ are often regulated within a small range, respectively, the realpower is roughly in proportion to the torque and the reactive power isroughly in proportion to the quorte.

In summary, the block Σ_(e) can be described as

$\Sigma_{e}\text{:}\left\{ {\begin{bmatrix}e \\{- T} \\{- \Gamma}\end{bmatrix} = {{\begin{bmatrix}0 & {\phi \; z} & 0 \\{{- \phi}\; z^{T}} & 0 & 0 \\{\omega \; z_{g}^{T}} & 0 & 0\end{bmatrix}\begin{bmatrix}i \\\omega \\\phi\end{bmatrix}}.}} \right.$

with z and z_(g) obtained via (3) and (1). Apparently, it is notskew-symmetric and not lossless, which causes considerable challenges inrendering the system passive.

For single-phase applications, only the first elements in the vectors z,z_(g), e and e_(g) are needed. For multiple-phase applications, thevectors z, z_(g), e and e_(g) can be adjusted according to the number ofphases to reflect the phase spacing. The vector z and, hence, the outputvoltage e contain equally spaced sinusoidal signals that can berepresented by the linear combination of the oscillator states. Inpractice, filters may be introduced to filter out the ripples in T and Γbefore feeding back.

Generation of Desired Frequency ω_(d) and Flux φ_(d) Through DroopControl:

The purpose of the blocks Σ_(ω) and Σ_(φ) in FIG. 2 is to generate thefrequency ω and flux φ according to the desired frequency ω_(d) anddesired flux φ_(d), which are designed according to the well-known droopcontrol principle as

ω_(d)=ω_(r) +D _(ω)(T _(set) −T),

φ_(d)=φ_(r) +D _(φ)(Γ_(set)−Γ).  (10)

Here, ω_(r) and φ_(r) are the frequency reference and the fluxreference, respectively, and D_(ω) and D_(φ) are the frequency droopcoefficient and the flux droop coefficient defined, respectively, as

$\begin{matrix}{{D_{\omega} = \frac{\Delta\Omega}{\Delta \; T}},{D_{\phi} = {- \frac{\Delta\phi}{\Delta\Gamma}}}} & (11)\end{matrix}$

to describe the impact of the torque variation ΔT, corresponding to theactive power variation ΔP, and the quorte variation ΔΓ, corresponding tothe reactive power variation ΔQ, on the frequency variation Δω and theflux variation Δφ. The reference values ω_(r) and φ_(r) are obtained viaadding the outputs of the integrator blocks I_(ω) and I_(φ) as offsetsto the rated values of the frequency and the flux

$\begin{matrix}{{\omega_{n} = {2\pi \; f_{n}}},{\phi_{n} = \frac{\sqrt{2}V_{n}}{\omega_{n}}},} & (12)\end{matrix}$

respectively, where f_(n) and V_(n) are the rated values of the systemfrequency and the phase voltage (rms). Note that D_(ω) and D_(φ)described above are static gains but they can be designed to be dynamicas well. e.g. to include an integrator or to be a filter.

Design of Σ_(ω) and Σ_(φ) to Obtain a Passive Σ_(C):

It can be shown that the block Σ_(C) in FIG. 2 is passive if the desiredfrequency and flux are designed as in (10) and the blocks Σ_(ω) andΣ_(φ) are designed to be passive as described by

$\begin{matrix}{\Sigma_{\omega}\text{:}\left\{ \begin{matrix}{{\overset{.}{x}}_{\omega} = {{\left( {J_{\omega} - R_{\omega}} \right)\frac{\partial H_{\omega}}{\partial x_{\omega}}} + {\frac{1}{D_{\omega}}G_{\omega}\omega_{d}}}} \\{{{\omega = {G_{\omega}^{T}\frac{\partial H_{\omega}}{\partial x_{\omega}}}},}\mspace{205mu}}\end{matrix} \right.} & (13) \\{E_{\phi}\text{:}\left\{ \begin{matrix}{{\overset{.}{x}}_{\phi} = {{\left( {J_{\phi} - R_{\phi}} \right)\frac{\partial H_{\phi}}{\partial x_{\phi}}} + {\frac{1}{D_{\phi}}G_{\phi}\phi_{d}}}} \\{{{\phi = {G_{\phi}^{T}\frac{\partial H_{\phi}}{\partial x_{\phi}}}},}\mspace{194mu}}\end{matrix} \right.} & (14)\end{matrix}$

with non-negative Hamiltonians H_(ω) and H_(φ), positive semi-definitedamping matrices R_(ω) and R_(φ), and skew-symmetric matrices J_(ω) andJ_(φ).

Moreover, it can be mathematically proven that the system shown in FIG.1 with the controller designed in FIG. 2 as characterized by the blockΣ_(C) and the engendering block Σ_(e) (9) is passive and stable.

Regulation and Self-Synchronization Capabilities:

As is well known, the most important and basic requirement forgrid-connected converters is to keep synchronized with the grid beforeand after being connected to the grid so that (1) the converter can beconnected to the grid and (2) the converter can exchange the rightamount of power with the grid even when the grid voltage changes itsfrequency, phase and/or amplitude. It has been a norm to adopt asynchronization unit. e.g. a phase-locked loop (PLL) and its variants,to make sure that the converter is synchronized with the grid. Thedisclosed controller shown in FIG. 2 is able to achieveself-synchronization before being connected to the grid withoutmeasuring or estimating the grid frequency.

The virtual impedance Z(s) is added to generate a virtual current i_(v)before being connected to the grid, according to the voltage differencebetween two voltages. e.g. e and v. The two integrator blocks I_(ω) andI_(φ) regulate T=T_(set) and Γ=Γ_(set), respectively. If T_(set) andΓ_(set) are set as 0, then both T and Γ can be regulated to 0 whenSwitch S_(C) is at Position 1. This leads to e=v and, hence, theconverter is synchronized with the grid. Once the synchronization isachieved, the converter can be connected to the grid. While theconverter is connected to the grid, Switch S_(C) is thrown to Position2. Then, the converter can be operated in the set mode to regulate T andΓ to the set-points T_(set) and Γ_(set), respectively, if the integratorblocks I_(ω) and I_(φ) are enabled by setting the signals S_(ω) andS_(φ) low; it can be operated in the frequency and flux droop mode ifthe integrator blocks I_(ω) and I_(φ) are reset by setting the signalsS_(ω) and S_(φ) high. The operation modes of the system are summarizedin Table I.

The integrator blocks I_(ω) and I_(φ) can be a simple integrator with again or a more complex transfer function consisting of an integrator, again and an additional transfer function. The gains should be small inorder to make sure that the desired frequency ω_(d) and flux φ_(d)change more slowly than the tracking of the frequency and the flux. Thevirtual impedance Z(s) can be chosen as a low-pass filter or otherimpedance that is appropriate.

While the output voltage e is often directly used as the control signalfor the power electronic converter, another option is to add the signali, onto the output voltage e before using it as the control signal. Inthis way, it is equivalent to adding an inner voltage loop to regulatethe voltage v to be the same as the output voltage e. Effectively, theactual control signal becomes e+i_(v). This helps eliminate theuncertainties in the converter hardware. e.g. the variations in theDC-bus voltage, the filter inductor and the power semiconductorswitches. It is also able to shape the output impedance of the converterby designing Z(s).

TABLE I OPERATION MODES OF THE DISCLOSED CONTROLLER IN FIG. 2. S_(C)S_(ω) S_(φ) Mode 1 Low Low Self-synchronization 2 Low Low Regulation ofT (hence, P) and Γ(hence, Q) 2 Low High Regulation of T and Droop of φ(hence, voltage) 2 High Low Droop of ω and Regulation of Γ 2 High HighDroop of ω and φImplementation of the Blocks Σ_(ω) and Σ_(φ)

The function of the blocks Σ_(ω) and Σ_(φ) is to track the desiredfrequency ω_(d) and flux φ_(d). There are many options to achieve this.Here, two examples are illustrated. One is to adopt the standardintegral controller and the other is to adopt a simple staticcontroller.

Using the Standard Integral Controller (IC):

FIG. 3 illustrates the implementation with the integrator for the blocksΣ_(ω) and Σ_(φ). It is easy to find that

$\begin{matrix}{{\Sigma_{\omega} = \frac{1}{{\tau_{\omega}s} + 1}},{\Sigma_{\phi} = \frac{1}{{\tau_{\phi}s} + 1}},} & (15)\end{matrix}$

where τ_(ω) and τ_(φ) are the time constants of the frequency and fluxloops, respectively. Both Σ_(ω) and Σ_(φ) are first-order low-passfilters with a unity static gain. The Hamiltonians can be chosen as

${H_{\omega} = {\frac{1}{2}\frac{\tau_{\omega}}{D_{\omega}}\omega^{2}}},{{{and}\mspace{14mu} H_{\phi}} = {\frac{1}{2}\frac{\tau_{\phi}}{D_{\phi}}{\phi^{2}.}}}$

Then, their time derivatives are, respectively,

${\frac{\partial H_{\omega}}{\partial\omega} = {\frac{\tau_{\omega}}{D_{\omega}}\omega}},{{{and}\mspace{14mu} \frac{\partial H_{\phi}}{\partial\phi}} = {\frac{\tau_{\phi}}{D_{\phi}}{\phi.}}}$

As a result, the block Σ_(ω) can be written in the form of (13) with

${J_{\omega} = 0},{R_{\omega} = \frac{D_{\omega}}{\tau_{\omega}^{2}}},{{{and}\mspace{14mu} G_{\omega}} = \frac{D_{\omega}}{\tau_{\omega}}}$

while the block Σ_(ω) can be written in the form of (14) with

${J_{\phi} = 0},{R_{\phi} = \frac{D_{\phi}}{\tau_{\phi}^{2}}},{{{and}\mspace{14mu} G_{\phi}} = {\frac{D_{\phi}}{\tau_{\phi}}.}}$

Using the Static Controller:

The simplest implementation is to use the static controllers

Σ_(ω)=1 and Σ_(φ)=1.  (16)

This is equivalent to the implementation with an integrator having zerotime constant in the previous subsection.

In this case, the output voltage (4) becomes

e=φ _(d)ω_(d) z.  (17)

TABLE II SYSTEM PARAMETERS, Parameter Value Parameter Value L₁, L₂ 2.5mH, 1 mH P_(set) 400 W R₁, R₂ 0.5 Ω Q_(set) 200 var C_(f) 22 μF RL loadR 54.45 Ω V_(n), f_(n) 110 V, 60 Hz RL load L 48 mH V_(g), f_(g) 112 V,59.8 Hz S_(n) 1 kVAValidation with Computational Simulations

The disclosed control framework is validated with computationalsimulations for the system shown in FIG. 1. The system parameters aregiven in Table II. The control parameters are determined as follows:

-   -   Droop of frequency: 1% of frequency variation for 100% of        variation in T (hence in P) resulting in

${D_{\omega} = {\frac{1\% \omega_{n}}{T_{n}} = {\frac{1\% \omega_{n}^{2}}{S_{n}} = 1.42}}};$

-   -   Droop of flux: 5% of flux (voltage) variation for 100% of        variation in Γ (hence in Q), resulting in

${D_{\phi} = {\frac{5\% \phi_{n}}{\Gamma_{n}} = {\frac{5\% \phi_{n}^{2}}{S_{n}} = {8.51 \times 10^{- 6}}}}};$

-   -   Time constants for the controller blocks Σ_(ω) and Σ_(φ):        τ_(ω)=0.002 s and τ_(φ)=0.02 s so that the frequency channel and        the flux channel have different time scales;    -   Gains of the integrators in the integrator blocks I_(ω) and        I_(φ): k_(ω)=11.84 and k_(φ)=4.32×10⁻⁴, which are commensurate        with D_(ω) and D_(φ).

The converter has the rated power S_(n)=1 kVA. The set-points for thetorque and quorte are obtained from

${T_{set} = {{\frac{P_{set}}{\omega_{n}}\mspace{14mu} {and}\mspace{14mu} \Gamma_{set}} = \frac{Q_{set}}{\phi_{n}}}},$

respectively. The simulation results with both the static controller(Static) and the integral controller (with IC) are shown in FIG. 4. Bothcontrollers perform very well. The static controller results in a fasterresponse with larger overshoots than the integral controller, asexpected because the static controller is equivalent to the case of theintegral controller with zero time constants τ_(ω) and τ_(φ).

Self-Synchronization:

This is mandatory before connecting the converter to the grid. Asmentioned before, it is the same as the set mode for the converter toregulate T and Γ to 0 using the virtual current i_(v), with the signalsS_(ω) and S_(φ) set at Low to enable the integrators. In order to showthe robustness of the synchronization, the initial grid voltage has aphase angle of +50°, a frequency of 59.8 Hz and a phase voltage of 112 V(rms value). As shown in FIG. 4, the converter voltage settles down at112 V and 59.8 Hz very quickly, achieving synchronization.

Operation after Synchronization:

After the converter achieves synchronization, it can be connected to thegrid. In order to demonstrate the proposed control framework, differentscenarios, including operation in both the grid-connected mode with gridfrequency and voltage changes and the islanded mode with load change,are tested. The results are shown in FIG. 4, with detailed descriptionsbelow:

-   -   t=1s, the Converter Breaker is closed with T_(set) and Γ_(set)        remained at 0 to regulate T and Γ (hence P and Q) at 0 in the        set mode. The physical current i is fed into the controller to        calculate T and Γ. It can be seen from FIG. 4 that there is a        very small and short transient, which means the grid connection        is very smooth.    -   at t=2 s, step on T_(set) to achieve P_(set)=400 W. The real        power quickly increases and settles down at the set point 400 W.        The flux φ and the voltages e_(a) and v_(a) all increase in        order to dispatch the required real power. The frequency f        increases in order to dispatch the increased real power but it        returns to the grid frequency very quickly. There is a small        coupling effect in Q but it quickly returns to 0 as well.    -   at t=3 s, step on Γ_(set) to achieve Q_(set)=200 var. The        reactive power Q quickly increases and settles down at the set        point 200 var. The voltage further increases because of the        increased reactive power. There is a small coupling effect in P        but it returns to normal very quickly.    -   at t=4 s, turn on the Load Breaker to connect the series RL load        of 54.45Ω and 48 mH (corresponding to 600 W and 200 var). There        are some short spikes in P and Q but they quickly return to the        original set-points of 400 W and 200 var because the converter        is still working in the set mode. The real power and reactive        power are not affected by the external condition. There is also        a small short spike in the frequency but it returns to normal        very quickly as well because the grid frequency remains        unchanged. The load voltage drops a bit because the load        increases, which causes the flux to decrease a bit too.    -   at t=5 s, the signal S_(ω) is changed to High to enable the        frequency droop. Because the grid frequency 59.8 Hz is below the        rated frequency 60 Hz, the converter increases the real power        automatically by

${\frac{0.2}{60} \times \frac{1000}{1\%}} = 333$

W to 733 W, attempting to regulate the grid frequency. However, the gridfrequency is fixed at 59.8 Hz so the frequency f quickly increases andreturns back to 59.8 Hz. The reactive power is still operated in the setmode so the reactive power quickly returns to 200 var after a smalltransient due to the coupling effect. The load voltage increasesslightly because the real power dispatched increases.

-   -   at t=6 s, the signal S, is changed to High to enable the flux        (voltage) droop. Because the voltage e_(a) is about 114 V, which        is above the rated voltage 110 V, the converter decreases the        reactive power automatically to regulate the voltage to a value        determined by the system parameters. For the system under        simulation, the reactive power is reduced by 500 var to −300        var, with the voltage e_(a) settling down at 112 V. The load        voltage v_(a) drops accordingly. The frequency is still        maintained by the grid at 59.8 Hz and the real power remains        more or less unchanged. Because of the change of the reactive        power, the current increases slightly.    -   at t=7 s, the grid frequency is changed to the rated value at 60        Hz. The frequency f quickly tracks the change of the grid        frequency and settles down at 60 Hz. Because the converter is        working in the frequency droop mode, the real power reduces        automatically by

${\frac{0.2}{60} \times \frac{1000}{1\%}} = 333$

W from 733 W to 400 W, the original set-point for the real power. Thiscauses the voltage e_(a) to drop a bit, which then causes the reactivepower to recover (increase) a bit.

-   -   at t=8 s, the grid voltage is changed to the rated value at        110 V. The voltage v_(a) drops below 110 V, which causes the        voltage e_(a) to drop too. As a consequence, the reactive power        increases. The real power and the frequency remain more or less        unchanged after a short transient.    -   at t=9 s, the grid is changed back to 59.8 Hz and 112 V and the        main breaker is opened to operate the converter in the islanded        mode. The change of the grid frequency and voltage does not        matter. What matters is the change of the operation mode from        the grid-connected to the islanded mode. As can be seen from        FIG. 4, the transition is very smooth. The real power increases        by 200 W to 600 W because of the load, which causes the        frequency to drop by

${1\% \times \frac{200}{1000} \times 60} = 0.12$

Hz to 59.88 Hz (from 60 Hz). The reactive power of the filter capacitoris about −300 var. Adding the load reactive power about 200 var, thereactive power is about −100 var. Taking into account the reactive powerof the filter inductor, the total reactive power is about −90 var, whichis consistent with the value shown in FIG. 4(b). The drop of thereactive power causes the voltages e_(a) and v_(a) and the flux toincrease slightly.

-   -   at t=10 s, an additional 200Ω load is connected to each phase        (corresponding to 180 W). The real power increases quickly and        the frequency drops by

${1\% \times \frac{180}{1000} \times 60} = 0.108$

Hz to 59.772 Hz. As expected, the change in the reactive power is verysmall and so are the changes of the flux V and the voltages e_(a) andv_(a).

As can be seen from the zoomed-in details of the transients, thetransients are very fast and often settle down within two cycles evenfor the integral controller (IC). The frequency and the flux only changewithin very small ranges. The torque T and the quorte Γ look verysimilar to the real power P and the reactive power Q, respectively,apart from having different values, and hence are not shown. It is worthnoting that the load voltage v_(a) is well maintained around the ratedvalue during the whole process, which is an important requirement.

It will be appreciated that variations of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. It will alsobe appreciated that various presently unforeseen or unanticipatedalternatives, modifications, variations or improvements therein may besubsequently made by those skilled in the art, which are also intendedto be encompassed by the following claims.

What is claimed is:
 1. A controller and method to operate a powerelectronic converter as a cyber synchronous machine (CSM, in short,cybersync machine), comprising a torque-frequency channel to generate afrequency signal according to the inputs consisting of a torqueset-point, a negative torque feedback signal and a frequency reference,a quorte-flux channel to generate a flux signal according to the inputsconsisting of a quorte set-point, a negative quorte feedback signal anda flux reference, an engendering block that takes the frequencygenerated in the torque-frequency channel, the flux generated in thequorte-flux channel and an input current to generate an output voltage,and a torque signal and a quorte signal for the negative torque andquorte feedback in the torque-frequency channel and the quorte-fluxchannel, respectively, a virtual impedance to generate a virtual currentaccording to the difference of two voltages, a switch to choose thevirtual current or an external current as the input current to theengendering block, a first integrator block with a reset input togenerate an offset signal that is added to the rated frequency to formthe frequency reference for the torque-frequency channel, and a secondintegrator block with a reset input to generate an offset signal that isadded to the rated flux to form the flux reference for the quorte-fluxchannel.
 2. A controller as claimed in claim 1 in which the engenderingblock contains an oscillator that generates sinusoidal and cosinusoidalsignals, as its states, with their frequency being the frequencygenerated by the torque-frequency channel.
 3. A controller as claimed inclaims 1 and 2 in which the engendering block generates a sinusoidalvector consisting of equally spaced sinusoidal signals, according to thenumber of phases of the converter, which are represented as the linearcombination of the sinusoidal and cosinusoidal signals generated by theoscillator.
 4. A controller as claimed in claims 1, 2 and 3 in which theengendering block generates the output voltage by multiplying thesinusoidal vector with the frequency generated in the torque-frequencychannel and the flux generated in the quorte-flux channel.
 5. Acontroller as claimed in claims 1 and 3 in which the engendering blockgenerates the torque signal by multiplying the flux with the innerproduct of the sinusoidal vector and the input current.
 6. A controlleras claimed in claims 1 and 2 in which the engendering block generates acosinusoidal vector consisting of equally spaced cosinusoidal signals,according to the number of phases of the converter, which arerepresented as the linear combination of the sinusoidal and cosinusoidalsignals generated by the oscillator.
 7. A controller as claimed inclaims 1 and 6 in which the engendering block generates the quortesignal by multiplying the opposite of the frequency with the innerproduct of the cosinusoidal vector and the input current.
 8. Acontroller as claimed in claim 1 in which the torque-frequency channelconsists of a first block that converts the sum of the torque set-pointand the negative torque feedback signal into an offset added to thefrequency reference to generate the desired frequency and a second blockto generate the frequency from the desired frequency.
 9. A controller asclaimed in claim 8 in which the first block is a constant gain calledthe frequency droop coefficient that reflects the impact of the torquevariation on the frequency variation.
 10. A controller as claimed inclaim 1 in which the quorte-flux channel consists of a third block thatconverts the sum of the quorte set-point and the negative quortefeedback signal into an offset added to the flux reference to generatethe desired flux and a fourth block to generate the flux from thedesired flux.
 11. A controller as claimed in claim 10 in which the thirdblock is a constant gain called the flux droop coefficient that reflectsthe impact of the quorte variation on the flux variation.
 12. Acontroller as claimed in claim 1 in which the virtual impedancerepresents the impedance of a complex network.
 13. A controller asclaimed in claim 1 in which one of the two voltages used to generate thevirtual current is the output voltage and the other is a voltagemeasured from the power electronic converter.
 14. A controller asclaimed in claim 1 in which the two voltages used to generate thevirtual current are both measured from the power electronic converter.15. A controller as claimed in claim 1 in which the first integratorblock with a reset input consists of an integrator in series with a gainand an additional transfer function.
 16. A controller as claimed inclaim 1 in which the second integrator block with a reset input consistsof an integrator in series with a gain and an additional transferfunction.
 17. A controller as claimed in claim 1 in which the resetfunction for the first integrator block and the second integrator blockis achieved by disconnecting or disabling the corresponding integratorblock.
 18. A controller as claimed in claim 1 in which the outputvoltage is used as the control signal for the power electronicconverter.
 19. A controller as claimed in claim 1 in which the outputvoltage and the virtual current are added together and used as thecontrol signal for the power electronic converter.
 20. A controller asclaimed in claim 1 in which the torque signal and the quorte signal arepassed through a filter, respectively, before completing the negativetorque and quorte feedback loops.